## EXPECTED UTILITY OF AN INVESTMENT

Once your utility function is specified, we can calculate the expected utility of an investment. This calculation involves multiplying the utile value of a particular outcome by the probability of its occurrence and adding together the product for all probabilities.

Illustrations:

Consider two investments that have cashflow streams and assonated probabilities.

Project A Project B

Cashflows Utiles Prob. Cashflows Utiles Prob.

Sh -20,000 -0.20 0.10 Sh -25,000 -0.25 0.10

0 0 0.10 0 0 0.20

60,000 0.60 0.60 50,000 0.50 0.50

80,000 0.80 0.50 100,000 1.00 0.20

The expected monetary value for Project A is

-20,000 (0.10) + 0(0.10) + 60,000 x (0.6) + 80,000 (0.20)

= Shs 50,000

For Project B

-25,000 (0.10) + 0 (0.20) + 50,000 (0.50) + 100,000 (0.20)

= Sh 42,500

Using the expected monetary value, Project A is preferred then Project B.

Using the utility values (utiles) the expected utility value is computed as follows:

Project A Project B

Utile Prob. Weighted Utile Prob. Weighted

Utility Utility

-0.20 0.10 -0.02 -0.25 0.10 -0.025

0 0.10 0 0 0.20 0

0.60 0.60 0.36 0.50 0.50 0.25

0.80 0.20 0.16 1.00 0.20 0.20

Expect utility value 0.540.425

Using utility values Project A should be accepted since it has a higher utility value.